Rear lights fuse

I think you are looking at the wrong fuse box.
Many today's cars have 2 fuse boxes. One under the hood (for mainly under the hood components) and another one under the dash just above your left knee area when you are sitting on the driver's seat. Check the one under the dash. Owner's manual would help.

 

Can someone tell me how to remove the driver's side fuse box cover on my 2020 Prius Prime. The pic in the manual is not very helpful

 

The brake lights work however. What is actually is the name for the wire, and where would it be able to be found?

 

See the Electrical Wiring Diagram (more info). As far as I know, Toyota doesn’t give the wires names or numbers in the service documentation; wires are identified by connector, terminal, and insulation color. The complete wire harnesses have part numbers, which are listed in the Electronic Parts Catalog, Figure 82-02, Wiring & Clamp, for the relevant model and year.